Park the mower on a level service and turn the engine off. Place a block in front of the front wheels to keep the mower from moving when you lift it.
Raise the side of the mower with the flat tire using the hydraulic jack. Be sure the jack is under the frame of the riding mower and not a fender. When you raise the mower, the tire should clear the ground by at least four inches.
Support the raised end of the mower with wooden blocks. Use as many blocks as necessary to help support the mower while it is up on the jack.
Pry off the plastic axle cover from the rear wheel, using a flat-head screwdriver. Remove the snap ring from the axle of the riding mower, using a pair of needle-nose pliers. Remove the washers from the axle.
Remove the square key from the wheel, using a pair of vise-grip pliers to grasp it and pull it out. Pull the wheel off the shaft and set it aside.